| 一类食饵具有常投放的稀疏效应捕食系统的定性分析 |
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| 引用本文： | 杜超雄,袁月定.一类食饵具有常投放的稀疏效应捕食系统的定性分析[J].系统科学与数学,2009,29(5):686-692. |
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| 作者姓名： | 杜超雄 袁月定 |
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| 作者单位： | 1. 邵阳学院数学系,邵阳,422000;中南大学数学学院,长沙,410083
2. 宜春学院数学系,宜春,336000 |
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| 基金项目： | 国家自然科学基金，湖南省教育厅科研项目 |
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| 摘 要： | 研究一类食饵具有常投放的稀疏效应捕食系统{dx/dt=bx2(k-x)-bxy+h,dy/dt=-cy+(βx-αy)y,得到了存在唯一极限环和不存在极限环及系统全局渐近稳定的充要条件.
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| 关 键 词： | 稀疏效应 捕食系统 极限环 全局渐近稳定. |
| 收稿时间： | 2007-3-21 |
| 修稿时间： | 2008-1-2 |
The Qualitative Analysis of a Predator-Prey System with Scanty Effect for the Constant Invest of Prey |
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| DU Chaoxiong,YUAN Yueding.The Qualitative Analysis of a Predator-Prey System with Scanty Effect for the Constant Invest of Prey[J].Journal of Systems Science and Mathematical Sciences,2009,29(5):686-692. |
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| Authors: | DU Chaoxiong YUAN Yueding |
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| Institution: | (1)Department of Mathematics, Shaoyang University, Shaoyang 422000; School of Mathematics, Central South University, Changsha 410083;(2)Department of Mathematics,Yichun University, Yichun 336000. |
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| Abstract: | In this paper, the following predator-prey system with scanty effect is considered: $$ \left\{\begin{array}{ll} \d \frac{{\rm d}x}{{\rm d}t}=bx^2(k-x)-bxy+h,\\2mm] \d \frac{{\rm d}y}{{\rm d}t}=-cy+(\beta x-\alpha y)y, \end{array} \right. $$where the prey species possesses a constant invest. The sufficient and necessary conditions for the existence and uniqueness of limit cycle surrounding the positive equilibrium point and for the global stability of the system are obtained. |
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| Keywords: | Scanty effect predator-prey system limit cycle global stability |
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